Sept 14, 20016 - Ryder Scott Conference

12th Annual Ryder Scott Reserves Conference | September 14th, 2016 | Houston, TX
MACHINE LEARNING FOR PRODUCTION FORECASTING:
ACCURACY THROUGH UNCERTAINTY
12TH ANNUAL RYDER SCOTT RESERVES CONFERENCE
SEPTEMBER 14TH, 2016
HOUSTON, TX
DAVID FULFORD
APACHE CORPORATION

PRODUCTION FORECASTING IN UNCONVENTIONALS
2

WE NOTICED A PROBLEM
3

IDENTIFYING CAUSES
 The Modified Hyperbolic model is not appropriate
for these wells
 Develop a new model
 Least error fitting is not a best fit and does not yield
a best forecast
 Develop a new fitting methodology
 Production surveillance is not possible given the
magnitude of wells that need forecasting every
quarter
 Develop a new workflow
4

IDENTIFYING CAUSESIDENTIFYING CAUSES SOLUTIONS

OUTLINE
 Problem Statement
 Model Foundation
 Model Regression / Parameter Estimation
 Machine Learning
 ‘Representative’ Forecasts & Type Wells
 Case Studies
6

PROBLEM STATEMENT
 Our forecasting was yielding unreliable results
 Low permeability leads to long duration transient
regimes
 Production decline behavior differs significantly in
 transient vs.
 transitionary vs.
 boundary-dominated regimes
 Most models are formulated to forecast a single,
specific regime
7

IS WHAT WE’RE DOING WORKING WELL ENOUGH?
 The overwhelmingly popular model for reserves
forecasting is the modified hyperbolic model
 First segment
 𝑞 = 𝑞𝑖 1 + 𝑏𝐷𝑖 𝑡
−1
𝑏 𝑓𝑜𝑟 0 < 𝑏 ≤ 2
 Second segment
 𝑞 = 𝑞𝑖 𝑒−𝐷𝑡 𝑡 𝑓𝑜𝑟 𝑏 = 0
 Switch time
 𝑡 𝑠𝑤 =
1
𝐷 𝑡
−1
𝐷 𝑖
𝑏
 General agreement that 𝑏 = 2 is not appropriate for this
model
8

 Extrapolating Transient Data
 “Best fit” b = 1.55
 Looks good – Easy enough to meet production targets!
 Model EUR: 800 MMcf w/ 10% terminal decline
9

 Failure to recognize flow regime change
 Data EUR: 254 MMcf
 Model EUR: 800 MMcf w/ 10% terminal decline
 To get 254 MMcf for model, requires 78% terminal decline
10

 Valid Extrapolation only in the BDF regime
 b = 0.38
11

 For the specific case of forecasting life-cycle decline of
unconventional shale wells –
 No theoretical justification or convincing empirical validation of the
Modified Hyperbolic model
 SPEE Monograph 4 on the Modified Hyperbolic model –
 “The most likely failed constraint is constant fluid compressibility… this
breaks the theoretical link between exponential decline and all gas
wells and all oil wells that will ever produce below the bubble point.”
 “Potential bias will result if historical data are ignored and/or changing
flow regimes are not recognized with a decreasing b over time.”
 “Exponential tails are used once decline rates fall to values where
curves with different b factors are indistinguishable.”
12

 SPEE Monograph 4 on the Modified Hyperbolic model –
 “It does not honor the physics of flow during the transient flow
regime.”
 “Strong evidence to support an assumption of exponential decline
during BDF is scarce, despite widespread use of this practice.”
 “Use an appropriate transient flow model for matching “early” data
and use an appropriate BDF model for matching “late” data. Using the
Arps model with a minimum terminal (exponential) decline rate does
neither.”
 “…rules of thumb recommending specific values of any Arps
parameters are unlikely to yield greater precision than a
systematic evaluation of what causes the values of the 𝑞𝑖, 𝑏,
and 𝐷𝑖 in existing wells under consideration.”
13

 Unconventionally Complex
 Linear-to-Boundary Model
 Closed Linear Reservoir
 Real Fluids

𝑑(𝜇𝑐)
𝑑𝑡
≠ 0
 Flowing Bottom Hole Pressure
 Hyperbolic window
 Compound Linear Flow
 Contribution outside stimulated area
 Non-uniformity
 Heterogeneity, non-planar fractures
 Multi-Phase effects
 𝑝 𝑏 relative to 𝑝𝑖
MODEL FOUNDATION
14

 Linear-to-Boundary Model
 Analytic solution for:
 Slightly Compressible Fluid
 Constant Fluid Properties
 Homogeneous Matrix Properties
 Symmetrical Reservoir Geometry
 Infinite Fracture Conductivity
 No skin
 Constant FBHP
MODEL FOUNDATION
15

CLOSED LINEAR RESERVOIR
 Linear-to-Boundary model
16
Vardcharragosad et al. (2015)
 Linear Flow
 𝑞 ∝ 𝑡
1
𝑏 ; b-parameter = 2
 Transitionary regime
 Boundary-dominated flow
 b-parameter = 0
 b-parameter <= 0.5 for single
layer systems
 b-parameter > 0.5 typically as a
result of heterogeneity and/or
additional complexities
7x

TRANSIENT HYPERBOLIC MODEL (THM)
17
 Equivalent to analytic
solution for linear reservoir
 Early & late-time behavior
are derived from fluid flow
theory
 1 𝑞(𝑡) = 𝑞𝑖 𝑒
−𝐷 𝑖 0
𝑡 1
1 + 𝐷 𝑖 𝑏𝑡
𝑑𝑡
 Short Term Approx.:
 2 𝑞 𝐷 =
1
𝜋
2
𝑦 𝑒
𝑥 𝑒
𝜋𝑡 𝐷𝑦 𝑒
−1
2
 Long Term Approx.:
 2 𝑞 𝐷 =
1
𝜋
2
𝑦 𝑒
𝑥 𝑒
𝑒−
𝜋2
4
𝑡 𝐷𝑦 𝑒
 Short Term Approx.:
 2 𝑞 𝐷 =
1
𝜋
2
𝑦 𝑒
𝑥 𝑒
𝜋𝑡 𝐷𝑦 𝑒
−1
2
 Long Term Approx.:
 2 𝑞 𝐷 =
1
𝜋
2
𝑦 𝑒
𝑥 𝑒
𝑒−
𝜋2
4
𝑡 𝐷𝑦 𝑒
1Arps (1945) 2Wattenbarger et al. (1998)

TRANSIENT HYPERBOLIC MODEL (THM)
 Transitionary behavior empirically derived
2 𝑏 𝑡 = 𝑏𝑖 − 𝑏𝑖 − 𝑏𝑓 𝑒−𝑒
−𝑐 𝑡−𝑡 𝑒𝑙𝑓 +𝑒 𝛾
1 𝐷 𝑡 =
1
0
𝑡
𝑏𝑑𝑡
18
1Arps (1945) 2Fulford and Blasingame (2013)

THM PARAMETER DEFINITION
 3 𝑞𝑖 =
𝑥 𝑓ℎ(𝑝 𝑖−𝑝 𝑤𝑓)
31.28 𝐵
0.5
𝐷 𝑖
𝜇
𝑘𝜙𝑐 𝑡
−1
2
 3 𝐷𝑖 =
0.5
𝑡 𝑚
(∞ if no skin & infinite fracture conductivity)
 𝑏𝑖 = 2
 𝑏𝑓 = 0 (for constant 𝑐𝑡,𝜇)
 2 𝑡 𝑒𝑙𝑓 = 0.1
𝜙𝜇𝑐 𝑡 𝑖 𝑦 𝑒
2
0.00633𝑘
1 𝑞(𝑡) = 𝑞𝑖 𝑒
−𝐷 𝑖 0
𝑡 1
1 + 𝐷 𝑖 𝑏𝑡
𝑑𝑡
19
1Arps (1945) 2Fulford and Blasingame (2013) 3Fulford et al. (2016)

 Real Fluids
 Viscosity and Compressibility
vary with density
 Density varies with pressure
 Pressure varies with time
MODEL FOUNDATION
20

THEORETICAL EXPECTATION OF B-PARAMETER
 Theoretical basis for 0 ≤ 𝑏 ≤ 1 provided by Ayala
and Ye (2013)
 “The availability of a predictive model for b… is a
significant finding that invalidates the commonly-held
assumption that decline exponents for gas wells (“b”) are
subject to empirical determination through best-fit of rate-
time gas well data. Rather, it is demonstrated that b-
decline exponents for gas wells can be explicitly calculated
a priori as a function of bottom hole pressure specification,
intrinsic viscosity-compressibility characteristics of the
fluid ( 𝐵), and viscosity-compressibility changes with time
(𝜆) and hence before any rate-time production data is
collected.”
21

 For the simplified case of 0 BHP, 𝑏 =
𝐵
1+ 𝐵
𝑝𝑖
𝑝 𝑤𝑓
𝐵 = 𝑠𝑙𝑜𝑝𝑒
22

 Pseudo-functions are typically employed to account for drive
energy of fluid expansion
23

 Flowing Pressure affects
decline behavior
 As average reservoir pressure
approaches flowing pressure,
fluids behavior emulates
constant properties
MODEL FOUNDATION
24

EFFECT OF FLOWING PRESSURE
pwf = 500
pwf = 0
 Decline is always hyperbolic for 𝑝 𝑤𝑓 = 0
 b eventually transitions to 0 for 𝑝 𝑤𝑓 > 0
25

HYPERBOLIC WINDOW
Hyperbolic
Window
 For 𝑝 𝑤𝑓 > 0, hyperbolic window exists before transition to
exponential decline
26

HYPERBOLIC WINDOW
Hyperbolic
Window
 Validation of Modified Hyperbolic model only in the BDF case
27

 Compound Linear Flow
 Contribution outside fracture
stimulated region
 May have less porosity &
permeability than “enhanced”
region
MODEL FOUNDATION
28

CONSIDERING COMPOUND LINEAR FLOW
 Clarkson et al. (2014) provide an approximation for a
composite reservoir as a summation of inner and outer
regions
 We can utilize this approach with our empirical model (THM)
ye
xf
yl
xl
ye
xf xl
yl
Beyond Fracture Tip (Tri-linear Model1) Between Fractures (EFR Model2)
29
1Brown et al. (1945) 2Stalgorova and Mattar (1945)

ENHANCED FRACTURE REGION MODEL1
𝑥 𝑟 =
𝑥 𝑓
𝑥𝑙
= 1 𝑦𝑟 =
𝑦𝑒
𝑥𝑙
= 0.83
ye = 25 yl = 30
xf = xl = 500
k1 = .001 k2 = .0001
𝑘 𝑟 =
𝑘1
𝑘2
= 10
𝑞 𝑇 = 𝑞1 + 𝑞2 𝑞2 =
𝑞 𝑇
𝑥 𝑓 𝑟 𝑘 𝑟 𝜙 𝑟
𝑡 𝑒𝑙𝑓2
=
𝑡 𝑒𝑙𝑓1 𝑘 𝑟
𝜙 𝑟 𝑦 𝑟
2 +
𝑡 𝑒𝑙𝑓1 𝜙 𝑟
𝑘 𝑟
2
30
1Stalgorova and Mattar (1945)

EARLY-TIME FLOWING PRESSURE CHANGES
Pressure,psi
Early-time ½ slope
masked by
decreasing BHP
bi
bf
bterminal
31

EFFECTS OF SPACING ON FLOW REGIMES
32
Well Spacing / Fracture Spacing
bf
0
2
bi
Boundary Dominated
Flow
Compound Linear Flow
Linear Flow
Boundary Dominated
Flow
b-parameter
(Boundary Influenced Flow)
bi
bf
bterminal

MFHW FLOW REGIMES
After Song & Ehlig-Economides (2011)
Boundary
Dominated
Flow
Transient
Linear
Flow
Boundary
Dominated
Flow
Fracture
Storage
Compound
Linear Flow
b = 4 b = 2 b < 1 b = 2 b < 1Inter-fracturepressureinterference
Pressure
Depletion in SRV
Inter-wellpressureinterference
Pressure
Depletion in
Reservoir
ye
xf
bi bf bterminal
33

DIAGNOSTICS / PRODUCTION SURVEILLANCE
𝒍𝒏 𝒒 = 𝒍𝒏 𝒒𝒊 −
𝟏
𝒃
𝒍𝒏 𝟏 + 𝑫𝒊 𝒃𝒕
𝒍𝒏 𝒒 = 𝒍𝒏 𝒒𝒊 − 𝑫𝒊 𝒕
Black dashed is
remaining recoverable
De-noise data while maintaining
reservoir signal
Straightlineswhen𝒃=𝑪𝒐𝒏𝒔𝒕𝒂𝒏𝒕
34

DIAGNOSTICS / PRODUCTION SURVEILLANCE
𝑩𝑫𝑭 = 𝑯𝒂𝒓𝒎𝒐𝒏𝒊𝒄
only if pseudo-time/pseudo-pressure
Highlights “bad” data
points
Increase in effective Decline
Rate as 𝒕 → 𝒕 𝒃𝒅𝒇
𝒃 = 𝚫𝒃𝒆−𝒆−𝒄𝒕
𝒄 = 𝒇 𝒕 𝒆𝒍𝒇
𝑫 𝒆𝒇𝒇 = 𝟏 − 𝟏 + 𝒃𝑫
−𝟏
𝒃 =
𝒒𝒊 − 𝒒 𝟏
𝒒𝒊
35

EMPIRICAL VALIDATION
Eagle Ford Marmaton
Granite Wash Woodford
36

EMPIRICAL VALIDATION
Wolfcamp Cleveland
Bakken Bluesky
Kaybob
37

EAGLE FORD HINDCASTING
 Apache was one of the first movers in the Eagle Ford
 Surprised?
 8 wells drilled in 2008, among the oldest MFHW
liquids-rich shale wells
38

39

40

MODEL REGRESSION
 SPEE Monograph 4 –
 “If there is no evidence of BDF in the available data, we cannot
establish with certainty when linear flow will end…”
 “We do not know with certainty what value of b is appropriate in the
BDF regime.”
 Flow regime diagnosis is implicit in regression of the model
 𝑡 𝑒𝑙𝑓 and 𝑏𝑓 must still be estimated if within the transient flow
regime
41

MODEL REGRESSION
 The 𝑡 𝑒𝑙𝑓 parameter is analytically defined
 but empirically regressed
 The 𝑏𝑓 parameter has some theoretical justification for a
certain range of values
 but is still an empirically derived parameter
 lumps many non-idealities together
 First preference
 estimate from analogs
 Second preference
 use knowledge and experience from practiced application of the
model
 Decline Curve Analysis entails an implicit expression of bias!
42

MACHINE LEARNING & UNCERTAINTY
43

WHAT IS MACHINE LEARNING?
 Machine learning is a name given to algorithms and
techniques for the extraction of predictive models
from data
 Unsupervised learning extracts structure, grouping,
and dimension reduction from correlations and
clusterings in unlabeled data
 Supervised learning works in labeled data sets to
learn models which can
 map one or more predictors to one or more targets
44
predict values for future
unobserved data

NOT AUTOMATED FORECASTING
 Our problem:
 given observed data of well performance vs. time,
 learn an appropriate forecast model
 to predict future well performance
 Time-rate data are indirect observations of fluid &
rock properties
 Non-unique inverse problem
 Many local optimums such that a
45
least error fit is not a
best fit and does not yield a best forecast

SOLUTION SPACE OF INVERSE PROBLEMS
 Markov Chain Monte Carlo Simulation
 Proven technology with 20+ years of use in oilfield
 Reservoir simulation –
 Model selection
 Model calibration
 Uncertainty quantification
 Seismic inversion / seismic processing
 Estimation of model parameters required to
guide/constrain the solution set
46

MARKOV CHAIN MONTE CARLO
 Other applications –
 Cryptography
 Text decryption
 Astronomy
 Analysis of CMB to determine age of the Universe
 Meteorology
 Hurricane risk assessment
 Chemistry
 Nanoscale research in phase behavior
 etc. etc. etc.
47

MCMC EXAMPLE
 MCMC example for a case with an exact solution –
 Cryptography
 Propose a function for likelihood of one letter appearing after another
 Randomly change cipher
 Accept steps that are more likely, conditionally accept steps that are
less likely
Text Decryption using MCMC. Statistically Significant. http://alandgraf.blogspot.com/2013/01/text-decryption-using-mcmc.html
48

MCMC EXAMPLE
 With enough indirect observation, and enough
iterations, the Markov chain converges to solution
Diaconis, P. 2008. The Markov Chain Monte Carlo Revolution. Bull. Amer. Math. Soc., Nov. 2008.
49

PRODUCTION FORECASTING MARKOV CHAINS
EUR Iterations
IP Iterations
Di Iterations
bi Iterations
bf Iterations
telf Iterations
50

INFERENCE
 MCMC Inference is inherently Bayesian
 Bayes’ Theorem infers between our prior knowledge
& beliefs and new data we acquire.
 Avoids base rate fallacy – disregarding general
information and overvaluing specific information
 THM provides a generalized solution for time-rate
performance
 Production history provides specific data on time-rate
performance
 From belief of the general behavior, converge to the
specific behavior
51

 10,000+ possible forecasts are summarized into
discrete percentiles
DISTRIBUTION OF FORECASTS
52
Actual vs. MCMC Forecasts
Time
Rate

53
 Possible fits of data + uncertainty of future
performance
Actual vs. MCMC Forecasts
Time
Rate

 Representative Forecasts
 What are the features of the set of forecasts that recover
the P50 volume?
54
Log Rate vs. Log Time Log Rate vs. Time

ELM COULEE EVALUATION
 Elm Coulee field, in the Bakken play, is used as a
verification of the method
 Long production history of at least 5 years
 136 wells with discernable and consistent trend are
selected
 Re-fracs or other significant changes in production trend
are excluded
55

Example of hindcasts for an Elm Coulee well, known 𝒃 𝒇 & MLE = High
Log Rate vs Log Time Log Rate vs Time
56

Base Case Known bf Biased Low bf
𝑫𝒊 Minimum 35% 35% 35%
𝑫𝒊 Maximum 95% 95% 95%
𝒃𝒊 2 2 2
𝒃 𝒇 Min 0 0 0
𝒃 𝒇 Max 1.5 1.5 1.5
𝒕 𝒆𝒍𝒇 Min (days) 5 5 5
𝒕 𝒆𝒍𝒇 Max (days) 35 35 35
𝒃 𝒇 MLE n/a 1.0 0.5
Comparison of P50 Hindcast versus Actual 5 year
cumulative production
Prior Distribution parameters for the scenarios
used to hindcast 136 Bakken wells
Hindcast vs Actual
5 Year Cum. Production
57 MLE = Maximum Likelihood Estimate

GOOD ESTIMATES ACCELERATE CONVERGENCE
 Comparison with and without prior information
 time to end of linear flow (telf)
 P90 = 10 days, P10 = 40 days
EUR
EUR
Months of Data Used for Fit Months of Data Used for Fit
58

QUANTIFYING UNCERTAINTY
 As we gain more data, uncertainty in the forecast decreases
 Quantifying uncertainty allows decisions to incorporate the
reliability of information (production data)
59

TYPE WELL METHODOLOGY
1. Unequal production histories?
2. Shut-in wells? (Freeborn et al. 2012)
3. Flush production after shut-in?
4. High bias inherent in arithmetic means?
5. summing exponentials = hyperbolic, summing hyperbolics =
more hyperbolic (Fetkovich et al. 1996)

TYPE WELL CALCULATION
61
P10 P50 P90 P10 P50 P90 P10 P50 P90 P10 P50 P90 P10 P50 P90 P10 P50 P90
Well Data
P10 P50 P90
Well Forecasts
Type Well

TYPE WELL VALIDATION
 Type Well on public data
vs
 Technical workflow (petrophysics, DFIT, fracture modeling,
RTA, PVT model)

USING THE DATA SET
 The Type Well is the “representative well” that may
be used as the basis for forecasting early-time data,
as well as verifying reliability of forecasts for any
well.
63

WOLFCAMP EVALUATION
 The Wolfcamp play in the Permian basin is one of the
most active plays in the U.S.
 Over 10 million acres, 25% of all U.S. onshore rigs (2014)
 Analysis of statistically significant sample sizes of
wells completed with low proppant loading (85
wells) and high proppant loading (39 wells)
64

WOLFCAMP EVALUATION
Histogram of EUR for Low Proppant Loading and
High Proppant Loading completion strategies
Histogram of EUR
65

WOLFCAMP EVALUATION
Histogram of IP30, b) regression of IP30 vs EUR shows no correlation
Histogram of IP30 IP30 vs EUR
66

WOLFCAMP EVALUATION
a) Histogram of 𝒒𝒊, b) regression of 𝒒𝒊 vs EUR shows almost no correlation
Histogram of qi qi vs EUR
67

WOLFCAMP EVALUATION
a) Histogram of 𝑫𝒊, b) histogram of 𝒃 𝒇
Histogram of Di Histogram of bf
68

WOLFCAMP EVALUATION
High vs Low Proppant-Load Type Wells
Comparison of High Proppant Loading vs Low Proppant Loading P50 Type Wells
69

APACHE’S UCR PRODUCTION FORECASTING TOOL
RATE ANALYTICS WITH PROBABILISTIC INFERENCE
& DIAGNOSTICS
DIAGNOSTICS
PROBABILISTIC FORECASTING
PROBABILISTIC TYPE WELL CREATION
70

 The Modified Hyperbolic model is not appropriate
for these wells
 The Transient Hyperbolic model can reasonably
approximate the complex behavior of these wells
 Least error fitting is not a best fit and does not yield
a best forecast
 MCMC generates a true reserves-based forecast
 Production surveillance is not possible given the
magnitude of wells that need forecasting every
quarter
 The speed of the machine-based approach and use of the
diagnostic dashboard leads to more reliable forecasts
71
IDENTIFYING CAUSESIDENTIFYING CAUSES SOLUTIONS

Questions?
72

REFERENCES
 Arps, J.J. 1945. Analysis of Decline Curves. Transactions of the AIME 160 (1): 228–247. SPE-945288-G.
http://dx.doi.org/10.2118/945228-G.
 Brown, M., Ozkan, E., Raghavan, R., and Kazemi, H. 2011. Practical Solutions for Pressure-Transient Responses of Fractured
Horizontal Wells in Unconventional Shale Reservoirs. SPE Res Eval & Eng 14 (6): 663–676. SPE-125043-PA.
http://dx.doi.org/10.2118/125043-PA.
 Clarkson, C.R., Williams-Kovacs, J.D., Qanbari, F., Behmanesh, H., and Sureshjani, M.H., 2014. History-Matching and
Forecasting Tight/Shale Gas Condensate Wells Using Combined Analytical, Semi-Analytical, and Empirical Methods.
Presented at SPE/CSUR Unconventional Resources Conference – Canada in Calgary, Alberta, Canada, 30 September–2
October. SPE-171593-MS. http://dx.doi.org/10.2118/171593-MS.
 Fulford, D.S., and Blasingame, T.A. 2013. Evaluation of Time-Rate Performance of Shale Wells Using the Transient Hyperbolic
Relation. Presented at SPE Unconventional Resources Conference in Calgary, Alberta, Canada, 5–7 November. SPE-167242-
MS. http://dx.doi.org/10.2118/167242-MS.
 Fulford, D.S., Bowie, B., Berry, M.E., and Bowen, B. 2016. Machine Learning as a Reliable Technology for Evaluating
Time/Rate Performance of Unconventional Wells. SPE Econ & Mgmt 8 (1): 23–29. SPE-174784-PA.
http://dx.doi.org/10.2118/174784-PA.
 Song. B, and Ehlig-Economides, C.A., 2011. Rate-Normalized Pressure Analysis for Determination of Shale Gas Well
Performance. Presented at SPE North American Unconventional Gas Conference and Exhibition in The Woodlands, Texas,
USA, 14–16 June. SPE-144031-MS. http://dx.doi.org/10.2118/144031-MS.
 Stalgorova, E., and Mattar, L. 2012. Pratical Analytical Model to Simulate Production of Horizontal Wells with Branch
Fractures. Presented at SPE Canadian Unconventional Resources Conference in Calgary, Alberta, Canada, 30 October–1
November. SPE-162515-MS. http://dx.doi.org/10.2118/162516-PA.
 Vardcharragosad, P., Ayala, L.F., and Zhang, M. 2015. Linear vs. Radial Boundary-Dominated Flow: Implications for Gas-Well-
Decline Analysis. SPE J 20 (1): 1053–1066. SPE-166377-PA. http://dx.doi.org/10.2118/166377-PA.
 Wattenbarger, R.A., El-Banbi, A.H., Villegas, M.E. and Maggard, J.B. 1998. Production Analysis of Linear Flow Into Fractured
Tight Gas Wells. Presented at SPE Rocky Mountain Regional Low-Permeability Reservoirs Symposium and Exhibition in
Denver, Colorado, USA, 5–6 April. SPE-39931-MS. http://dx.doi.org/10.2118/39931-MS.
 Zhang, M., and Ayala H., L.F., 2014. Gas-Production-Data Analysis of Variable-Pressure-Drawdown/Variable-Rate Systems: A
Density-Based Approach. SPE Res Eval & Eng 17 (4): 520–529. SPE-172503-PA. http://dx.doi.org/10.2118/172503-PA.73

SUGGESTED QUESTIONS
 How likely do you see it for people to adopt machine
learning methods as a replacement for classical
decline curve analysis?
 Is this machine learning approach a “reliable
technology”?
74

APPENDIX
75

LINEAR FLOW DURATION
𝜙 = 4%
𝑘 = .0001 𝑚𝑑76

30-yr Cumulative Production, Mbbl
Posterior PDF Posterior CDF
77

 Reasonable assumption of linearity of parameters to EUR
78
Parameter Linearity
30-yr Cumulative Production
Residual of Linear Fits
30-yr Cumulative Production

CASE STUDIES
79

Convergence towards the Actual 5 year cumulative production
for the a) Base case and b) Known 𝒃 𝒇 case
Hindcast Convergence Hindcast Convergence
80

Predicted vs. Actual Quantile-Quantile Plot for Base case & Known 𝒃 𝒇 case
Prediction vs Actual Quantile-Quantile Plot Prediction vs Actual Quantile-Quantile Plot
81

ZAMA TYPE WELL EVALUATION
 Oil field in NW Alberta completed with vertical wells
 Well histories range between 6 months and 30+
years
 Transient Hyperbolic Model intended for MFHW, not
un-fractured vertical wells, but…
82

 Few wells have clean
histories
 Much of the data is quite
noisy
83
Log Rate vs Log Time Log Rate vs Log Time

 Some forecasts require little
adjustment
 Most wells require some
data filtering
84

 Combination of short…  …and long histories
85

86
 Comparison of RAPID type well vs industry-standard
of averaging normalized well data
 Abandoned wells report zero production
Log Rate vs Log Time Log Rate vs Time

 Non-uniformity
 Fractures and not uniform
length, or uniformly spaced
 Rock properties are not uniform
nor constant through time
MODEL FOUNDATION
87

NON-UNIFORM FRACTURE MODELS
Planar Fractures
900 – 1,300’ xf
Network Fractures
75’ spacing DFN
Network Fractures
50’ spacing DFN
Cipolla, C. Stimulated Reservoir Volume: A Misapplied Concept?, paper SPE 168596 presented at
2014 SPE Hydraulic Fracturing Conference, The Woodlands, Texas, USA, 4-6 February
88

89

UTICA
BARNETT, DELAWARE BASIN
NATURAL HYDRAULIC FRACTURE
BARNETT
Rassenfoss, S. What Do Fractures Look Like?, Journal of Petroleum Technology, v. 67,
Issue 5, May 2015
90

Rassenfoss, S. What Do Fractures Look Like?, Journal of Petroleum
Technology, v. 67, Issue 5, May 2015
91

92

NON-UNIFORM ROCK PROPERTIES
𝑞 ∝ 𝑘
𝑡 𝑒𝑙𝑓 ∝ 1
𝑘
𝑏𝑓 = 0.95
𝑏𝑓 = 1.1
93

NON-UNIFORM ROCK PROPERTIES
Core @ 7,928’ Core @ 8,016’
88’
Walls, J.D. Quantifying Variability of Reservoir Properties From a Wolfcamp Formation Core, paper
URTeC 2164633 presented at 2015 Unconventional Resources Technology Conference, San
Antonio, Texas, USA, 20-22 July
94

 Multi-Phase effects
 Create changes in rate &
apparent duration of flow
regimes
 Using only initial fluid properties
can lead to error
MODEL FOUNDATION
95

MULTI-PHASE EFFECTS
 For transient linear flow –
 If below dewpoint/bubble point, CGR/GOR will be
constant, single phase models valid
 For boundary dominated flow –
 CGR stays relatively constant, single phase models valid
 GOR does not stay constant, single phase models invalid
Clarkson, C.R. An Approximate Analytical Multi-Phase Forecasting Method for Multi-Fractured
Light Tight Oil Wells With Complex Fracture Geometry, paper URTeC 2170921 presented at 2015
Unconventional Resources Technology Conference, San Antonio, Texas, USA, 20-22 July
96

MULTI-PHASE EFFECTS
97

MULTI-PHASE EFFECTS
98

MULTI-PHASE EFFECTS
99

MULTI-PHASE EFFECTS
100

MULTI-PHASE EFFECTS
101

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